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Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs

  • Martin Eigel EMAIL logo , Johannes Neumann , Reinhold Schneider and Sebastian Wolf
Published/Copyright: July 25, 2018

Abstract

This paper examines a completely non-intrusive, sample-based method for the computation of functional low-rank solutions of high-dimensional parametric random PDEs, which have become an area of intensive research in Uncertainty Quantification (UQ). In order to obtain a generalized polynomial chaos representation of the approximate stochastic solution, a novel black-box rank-adapted tensor reconstruction procedure is proposed. The performance of the described approach is illustrated with several numerical examples and compared to (Quasi-)Monte Carlo sampling.

Award Identifier / Grant number: Matheon project SE13

Award Identifier / Grant number: Matheon project SE10

Funding statement: Research of Johannes Neumann was funded in part by the DFG Matheon project SE13. Research of Sebastian Wolf was funded in part by the DFG Matheon project SE10.

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Received: 2017-10-18
Revised: 2018-02-08
Accepted: 2018-05-02
Published Online: 2018-07-25
Published in Print: 2019-01-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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